This paper presents a new method for imaging the 3D microstructure of porous media. The method is based on high-resolution X-ray computer tomography (CT) where a cone-shaped, diverging X-ray beam is used to generate 2D transmission images Unlike traditional X-ray CT, a 3D reconstruction array is created directly instead of creating a series of 2D slices. This allows direct measurement of 3D geometric and topologic properties of porous media on a microscale. Our results also demonstrate the effectiveness of the high-resolution system for imaging the distribution of two fluid phases in the void space. The imaging system overcomes the limitations of current methods and has enormous potential for quantifying the microstructure of chaotic porous media.